Anisotropic gradient elasticity for modelling bone tissue

The analysis of the stresses surrounding a transverse fracture in a bi-material cortical–trabecular bone interface is performed. It is well known that using classical elasticity results in singular character of the stresses around the crack tip. A gradient enhanced constitutive relation, adapted for an anisotropic bone material, is used in this paper in order to remove these unrealistic singularities. Gradient elasticity models ensure realistic mechanical behaviour by introducing extra gradient term accompanied by length scale parameter that carry the information about the lower scale structure of a material.